Question

If $a^3 + b^3 + c^3 - 3abc = 126,$ a + b + c = 6, then the value of (ab + bc + ca) is:

• A. 8
• B. 7
• C. 5
• D. 9

Answer 1

Answer:

C. 5

Solution:

Given :

$a^3+b^3+c^3-3abc=126$ and  a + b + c = 6

Formula used :

$a^3+b^3+c^3-3abc=(a+b+c)[(a+b+c)^2-3(ab+bc+ca)]$

Calculations :

126 = 6 [(6)² - 3(ab + bc + ca)] 

21 = 36 - 3(ab + bc + ca)

3(ab + bc + ca) = 15 

⇒ ab + bc + ca = 5 

∴ The value of ab + bc + ca is equal to 5